The Boston mayoral campaign, marked during the preliminary election by a notable civility among its 12 contestants, has turned caustic in the race’s closing weeks, with phone calls floating negative messages against state Representative Martin J. Walsh hitting voters’ phones this week.

Those calls, which have been tied to a company with connections to Councilor at Large John R. Connolly, follow at least two negative fliers denouncing Connolly that were sent out by unions that support Walsh.

On Wednesday night, an unknown number of Boston voters received calls from interviewers who identified themselves as employees of BR Interviewing, according to multiple recipients. The calls raised questions about Walsh’s progressive credentials and his financial ties to labor unions. They asked recipients whether their votes would be affected if they learned that Walsh had filed legislation hurting the city’s finances, without specifying which bills were being discussed.

They also pointed to Walsh’s past participation in the South Boston St. Patrick’s Day parade, which does not allow groups supporting gay rights to march. Both Walsh and Connolly previously marched in the parade, but have since distanced themselves from the event.

Polling calls to voters are not uncommon in campaigns; frequently they ask voters a combination of positive and negative questions about both candidates involved to test the viability of different campaign messages. What is less typical is a call like this, one that polls on demographics and on strictly negative questions about one candidate, a sign that a campaign may be gearing up for an attack against the opponent.

Connolly would not comment Thursday on whether his campaign had anything to do with the calls. The telephone number that one recipient said appeared on his phone corresponds to a number for Braun Research of Princeton, N.J., a market research firm. The Better Business Bureau lists BR Interviewing as an alternate name for Braun Research. Connolly’s campaign finance documents show Braun was paid more than $18,000 in July for polling as a subcontractor for Connolly’s campaign.

Braun Research officials did not respond to messages left Thursday.

‘I was interested because the tone [of the phone call] was very negative . . . and it was very detailed,’

While refusing comment on the matter Thursday, Connolly instead told the Globe: “We are not running a negative campaign. We are not going to run a negative campaign. And I will never run a negative campaign.”

Asked if his team could categorically deny involvement with the calls, Connolly replied: “I don’t know anything about the particular phone call you’re talking about.”

Connolly’s campaign struck a similar tone when asked later Thursday about its connection to the calls. Spokeswoman Natasha Perez said in an e-mail, “We have not and will not run a negative campaign. Throughout this campaign there have been numerous polls asking questions about both candidates. Unlike the outside superPACs supporting Representative Walsh, we have not and will not resort to negative campaigning.”

Janet Hookailo, a former executive at a quasipublic state development agency who said she volunteered for Councilor Rob Consalvo’s campaign during the preliminary and intends to vote for Walsh, said she received a call after 6 p.m. Wednesday.

If she were an undecided voter receiving the call, the Hyde Park resident said, “I would begin to wonder if Marty Walsh was a really bad guy.”

“I was interested because the tone was very negative and the way the information was presented was in very negative terms, and it was very detailed,” Hookailo said of the call.

The phone calls came the night after a televised debate during which Connolly cited two waves of negative mailers containing inaccurate information sent by the Greater Boston Labor Council, which is backing Walsh. The direct mail pieces derided Connolly’s upbringing and mischaracterized the New York school where Connolly taught for two years.

Walsh had denounced the mailers and said he wanted them to stop. During Tuesday’s debate, Connolly pointed to the second wave of mailers as evidence that labor unions are not listening to Walsh, who has said that he would be better able to deal with unions because of his experience as a labor leader.

On Thursday, Walsh’s campaign spokeswoman said in a statement, “On the day that he held a press conference condemning negative campaigning, a polling company paid over $18,000 by John Connolly’s campaign made calls to residents of Boston spreading anonymous negative attacks against Marty Walsh and nothing else. John Connolly is saying one thing, but his polling firm is engaging in the same negative tactics that he is supposedly condemning.”

Despite his repeated insistence that he does not favor negative campaigning, Connolly has engaged in negative attacks in the past. While seeking a seat on the City Council in 2007, his campaign sent two rounds of fliers attacking Stephen J. Murphy. Both candidates were running for at-large seats; Murphy had beaten him in the race two years earlier.

The fliers did not indicate who had sent them. But Connolly later admitted to being behind them, prompting Murphy to call him “a documented sneak and a liar.” Both won at-large seats, and Murphy is now the body’s president.

Other than the stated affiliation with BR Interviewing, Wednesday night’s calls bore no other obvious ties to any mayoral campaign.

Josh Dawson, a Back Bay realtor and former Democratic candidate for state representative who is supporting Walsh in the final election, said he received one of the calls shortly after 5 p.m. Wednesday. Dawson said he had supported Councilor Michael Ross during the preliminary.

The caller inquired about how he would classify his political leanings, his ethnicity, and his socioeconomic class, Dawson said.

Michael Scully, a West Roxbury resident who said he doesn’t “really care for either of them,” said he received a similar call Wednesday.

Scully, who said he worked as a legislative assistant on behalf of the “three strikes law” last year, said the call had not swayed him in favor of either Connolly or Walsh. He said he had voted for a different candidate in the preliminary, but declined to say which one.